Zoubek Intentional Miss Free Throw - Probability Analysis

[-jk]

This has been touched on but not explicitly stated. Lance and Zoub both had 4 fouls. Zoub had already played a career high in minutes. I suspect the only analysis K did was that the game should be decided in regulation, and then how to win it. I think he really didn't want any part of OT.

-jk

[GODUKEGO]

Watch the two Butler players closest to the basket following the 2nd foul shot. One holds Lance in a bear hug, and one crackbacks Singler.

http://www.youtube.com/watch?v=nDmW988_5Jg

Still, if it were me, I'd try and make that 2nd FT.

Zoub does not have a very good poker face. Seems like he was holding back a grin and than looks over at the bench right before the second free throw. Showing the last shot at least five times, it is hard to believe neither announcer mentioned the cross body block by Howard on Kyle. It was a blatant foul. As a ref you have to have the fortitude to make that call regardless of the game situation. A foul is a foul is a foul!!!

[greybeard]

1. The odds. The odds are much better if he orders Z to miss on purpose before he walks to the line for the first. First, if he makes the first, no one in the building, and none of the heads, is expecting a deliberate miss, except for the other four players on the floor who know that their job is to force Butler into an off balance heave from half court. Were it not for the cross body block on Singler that Howard threw that inexplicably was not called, Hayward would have gotten off only an unseemly heave that would have hit nothing.

2. If Butler nevertheless makes, Dukes amasing accomplishments this year remain intact. No self recriminations for the rest of their lives, Z if he missed the second but not on purpose, or the entire team if Z makes, Butler gets 5 seconds to take it in, hit somebody who gets off a good look and ties it up.

If that happens, K and me we didn't like Duke's chances going into OT. Butler going in has all the momentum; singler, Scheyer and Smith had played mucho minutes, Smith missed a layup, a difficult one but one that he makes except if he's tired, in the final minute that would have sealed it, Singler short armed a 12 footer that would have sealed it, Z through a pass off an offensive rebound that would have sealed it practically out of the gym. Z had dodged a bullet for 9 plus minutes. Nope the odds were not good if the game went to OT and the risks were too great.

All that this team accomplished was on the line. Even now, as K understatedly put it during the post game news conference when asked about Butler's Cinderala story, 'We've got a pretty good story of our own." If the idiots in the media would only have looked, simply talking about Zoubek was the story of the year. add Singler's emergence as the best player in the college game, Nolan's emergence as I think perhaps the best offensive guard in the country (I would develop it further, but he shoots the 3-ball with anyone, is as good taking it to the rim either in the open court but more importantly in the half court as well as anyone, except maybe Wall, and here's where he separates himself, he has a mid range game off his own creation that is without peer. H is also a lock down defender, who is a stone cold warrier, who will get in the face of people twice his size if they are looking for trouble with any of his boys. I will save you the details regarding the others.

Add all this remarkable individual growth with the temendous growth of this group as a team, which K has said time and again will make these guys brothers for life. I think he means it.

Why put all that in the pot by playing for a possible OT rather than forcing the issue on your terms, when the odds are decidedly against a make, when your guys are deployed and Singler has shut down Harward all night and if lightening strike, none of what your players has accomplished is lost, or tarnished in the least. "The Gods were against them is what folks would intone, and no chance, none at all, that any of the kids he loves will be haunted by a single bad memory.

The guy in a snap made a brilliant decision to go all in when the other guy had to draw to a highly improbable inside straight. In doing so, he preseved what his team had earned. That none of the heads have figured this out is hardly surprising. They still haven't gotten it that Duke had been getting better and better each week, was playing better than anyone in the country coming into the tournament, and had the tournament lasted another two weeks who knows how good Duke would have been then.

This team has four maybe five NBAers and that is not counting a possible Dawkins and Curry or Ryan, all of whom if they make it will not surprise me, and Lance will surely have a stellar career oversees, if not in the Show if he continues as he began to during the tournament to look for its shot. They were, in the end, much more then their some of their parts, and had a leader who would make the daring of old Stonewall look like meek doings.

An absolutely brilliant call, missed by the idiots who call themselves experts.

[ice-9]

Actually, if you lower the percentage of making it off an inbounds play, you make it more likely that trying to MAKE the free throw is the right idea:

Intentional miss: 8% chance of Butler winning (based on your assumptions)

Attempted make:
60% make FT * 20% * 40% + 40% miss FT * 8% = 0.08

The smaller the difference between the probability of a made 3 between the inbounds scenario and the "scramble" scenario the more likely it is that attempting to make the FT is the right decision.

And as has been said, this doesn't consider two additional sub-scenarios after a make:
1. you foul a 3pt shooter and he makes it
2. you foul a dribbler and give them only two free throws.

Hi CDu, I didn't bother to factor in the probability of Zoubek unintentionally missing the free throw as all it does is lessen the spread between the two decisions, and even then not really by much.

As your analysis above shows, assuming the probability of making a shot off an inbound play is 20%, the overall outcome even factoring Zoubek's unintentional miss is still 8%. The probability of unintentionally missing the free throw isn't a critical variable, so I didn't include it to keep things simple.

Assuming you can accept the 8% probability of a half court shot, the key variables are thus
x = the probability of making a 3-point shot based on an inbound play
y = the probability of Butler winning in overtime

I used x = 33% and y = 40%, but acknowledge that x could be lower; as low as 20% to make the Zoubek miss a better decision as long as you believe Butler has a 40% chance of winning in overtime.

If you believe y is actually closer to 50%, then the intentional miss is the better decision as long as x = 16%. And 16% definitely feels low to me.

Again I'm trying to simplify the math here...a lot of stuff isn't being captured, but boiled to the essence of the situation we can see that there is no obviously better decision. That in of itself is surprising to me, as I had initially thought going for the free throw was easily the better thing to do.

[mike88]

Hi CDu, I didn't bother to factor in the probability of Zoubek unintentionally missing the free throw as all it does is lessen the spread between the two decisions, and even then not really by much.

As your analysis above shows, assuming the probability of making a shot off an inbound play is 20%, the overall outcome even factoring Zoubek's unintentional miss is still 8%. The probability of unintentionally missing the free throw isn't a critical variable, so I didn't include it to keep things simple.

Assuming you can accept the 8% probability of a half court shot, the key variables are thus
x = the probability of making a 3-point shot based on an inbound play
y = the probability of Butler winning in overtime

I used x = 33% and y = 40%, but acknowledge that x could be lower; as low as 20% to make the Zoubek miss a better decision as long as you believe Butler has a 40% chance of winning in overtime.

If you believe y is actually closer to 50%, then the intentional miss is the better decision as long as x = 16%. And 16% definitely feels low to me.

Again I'm trying to simplify the math here...a lot of stuff isn't being captured, but boiled to the essence of the situation we can see that there is no obviously better decision. That in of itself is surprising to me, as I had initially thought going for the free throw was easily the better thing to do.

I think 16% is about right, assuming we defend the inbounds pass and that we aim to stop the 3 point basket (ie we basically don't defend the 2). Based on similar situations (Duke-Kentucky a notable exception), the most common outcome is a steal on the pass or a near-steal and desperation heave.

In the end, I think it comes down to Kahneman and Tversky's observation from prospect theory- we are risk seeking for losses and risk averse for gains. In this case, the decision was framed in "loss" format and K chose the "risky" option.

[SCMatt33]

I just got home from Indy (Yay!) and read some, but apologize if this point has been mentioned. I read several comments about the chance of Zoubs unintentionally missing the second, thus producing the same scenario and lessening the impact of the decision. I have to disagree completely with this being the case. If Zoubs is trying to make the shot, we're going to set up our d, especially our guards to defend against a set play on a make. With no timeouts left I would expect a quick inbounds and no time to switch defenses. Since everyone was on board with the miss, we were able to set up our defense and force the half-court shot from the sideline. If the miss was unintentional, they might have gotten a better shot off.

[Starter]

Well, I'm glad to come back from a long day of celebrating Duke's victory and see that we're all in agreement that I'm 100% right about this whole thing. You guys had some decent points too. Props to all involved, let's go Duke!

[Reddevil]

I'm not sure if this has been mentioned yet, but duke did not score a FG in the last 4:47 of the game. The way things were going OT would have been a tough go. Still, I don't think I would have had the rocks to call it. K has the clout to take a chance like that (thank goodness!). I don't think math and probability had much to do with it. It was a sneak attack, and it worked. Like K said, "what the hell". CHAMPS!

[Neals384]

Another issues is the number of timeouts remaining. I don't think we had one, and I wouldn't have take one anyway to give Butler a chance to plan for its options.

Duke had one Timeout left. But I agree it would have been dumb to use it.

[Neals384]

One other thing that I questioned in the last few seconds - originally at 13.6 sec K had Zoubek guarding Hayward as the inbounder. Did anybody else flash back to Laettner v. UConn 1990? I didn't like the choice given that Zoubek would have had a difficult time staying with Hayward had he managed to get the ball inbounds. I would have rather had Singler or Thomas guarding Hayward's inbound pass there. Of course Butler wound up using their last timeout, so it worked out great.

After the Butler TO, Z still guarded the inbounds pass. But Singler picked up the defense on Hayward. Only after Hayward got past Singler did Z pick him up on the help defense.

[Neals384]

We had nobody else in the lane (or at least nobody but Zoubek tried for the rebound).

Thomas was in the lane, right side. He made no effort to get the rebound, and was in a bear hug anyway. Singler was in the lane, left side, for the first free throw, but stepped back to the top of the circle for the second.

[greybeard]

How many seconds did Laetner have? George for UConn? I don't know math, but 3.8 is much, much bigger than say 2, and there is the little matter that everybody on their side might reactively pauseor lean to the bsket again wasting precisous miliseconds or more. At a minimum, they have to be saying to themselves, "WTF," and likely make a stupid play, which exactly what 52 did in front of the entire free world except the refs didn't call or the game would have ended before any shot was even had. Stonewall Jackson.

Then, as I mentioned, the costs. The general decided where the stand would be made. It would be made on Duke's terms, with his players having to do what they do best, play smart and take away what is "good" for the other guy. He put it in the hands of his guys, took the responsibility if lightening struck, and walked away with a championship because the odds were with him, and because you don't put the rent money into the pot, ever, not if there is a better option. Make no mistake, putting it on Z to make 2 going in, giving Butler to "run" something they've practiced the entire season, would have been put the rent money and the title to your car into the pot. You put pressure on Z to make two, you up the odds of Butler's making back, and then your guys who were tiring badly have to go into OT with the other side pumped; if things don't work out, you have the pundits saying, "We were right all along, they had an easy path, are not the Duke of old, yadayadayada, and thus your guys have to live with such snipes forever.

Had lightening struck under the alternative scenario, nobody here would have wanted overtime, nobody. JK has that exactly right in his post above. The odds could not possibly have been better in an overtime for Duke than they were at that moment. K seized the moment. He always does, and that's why there is no one better.

[Reilly]

... and K chose the "risky" option.

I believe K chose the safe, rational option, based on his assessment of the probabilities.

K did not like Duke's chance in OT. K thought Butler would have a much better chance of making a 3 off an inbounds play than they would off of a scramble situation.

Given his assessment of Duke's chances in OT and Butler's ability to make a 3 inbounding (higher) v. scramble (lower), K made the absolutely rational, safe, correct-by-the-numbers choice which gave Duke the greatest chance of victory, in his mind. It worked.

[DevilHorns]

K on Mike and Mike radio this morning said some very interesting things:

(paraphrasing)

1) Win the game now. Doesn't look like we would win in OT given foul trouble, away game, momentum, etc.
2) Have the chance to control the outcome: If we hit the FT, then up 3, they can run their designed play to get a shot off. If we intentionally miss, we have our defensive assignments already prepared for whatever scraping offensive threat they put together.
3) Kyle got absolutely blasted by Howard. But of course no one would expect them to call a foul in that situation.
4) Coaching is done on gut instinct. In another situation, the right move would be to make the FT and go up 3 (would be the norm in this situation). There is no true wrong call here, given what and how much you weigh important aspects of this game.

[Troublemaker]

This has been touched on but not explicitly stated. Lance and Zoub both had 4 fouls. Zoub had already played a career high in minutes. I suspect the only analysis K did was that the game should be decided in regulation, and then how to win it. I think he really didn't want any part of OT.

-jk

An excellent point, and Coach K basically recited it word for word on Sportscenter this morning. He also said "overtime was not an alternative for us."

As I wrote before in this thread, based on how Duke had shot and played the previous few possessions leading up to the final one, and based on the momentum and crowd that Butler would've carried into overtime had they tied on a buzzer-beater, I really didn't like Duke's chances and emotional mindset heading into overtime.

[ice-9]

More on Coach K's own words (http://sportsillustrated.cnn.com/dan...ml?eref=fromSI)

DP: Looking back at your strategy to intentionally miss a free throw with 3.6 seconds left in the national title game. Would you have done it differently?

MK: First of all, you can do it a number of different ways. I think each game you have to know what the game has done thus far. The last nine minutes of that game [Brian] Zoubek played with four fouls. The last five minutes Zoubek and Lance Thomas played with four fouls. Going into overtime for me was not an alternative. I did not want to go into overtime.

DP: So you were playing for the win?

MK: They had no timeouts. I know how good they are and how well-schooled they are. They're going to have something really good after the make. They'll probably get something decent even if we foul them. It's going to produce a number of plays. The clock will start as soon as we miss and I had everybody set up to guard their guys.

After the miss, Zoubek jammed whoever got the rebound. And he missed and we jammed. Then Kyle [Singler] got blown out on the side and they got what I thought would have been the very best thing that they could have gotten -- that is a desperation half-court shot. I thought we could have played 3.6 seconds in the half court. It came close, but, Dan, that's what our game is. In another situation, I probably would have done another thing. I don't think you can say one is right, one is wrong. It's always the thing that turns out well that turns out to be right. But when you analyze, a lot of times you don't analyze what could have happened. If it goes into overtime it's not a good situation for us -- with David and Goliath, we're playing an away game, we're in foul trouble. Not to have a defeatist attitude, but I think we have a better chance of losing if that extreme happens and a better shot at winning if the extreme that occurred happens. So right or wrong, and that's why we're in it.

[DevilHorns]

More on Coach K's own words (http://sportsillustrated.cnn.com/dan...ml?eref=fromSI)

DP: Looking back at your strategy to intentionally miss a free throw with 3.6 seconds left in the national title game. Would you have done it differently?

After the miss, Zoubek jammed whoever got the rebound. And he missed and we jammed. Then Kyle [Singler] got blown out on the side and they got what I thought would have been the very best thing that they could have gotten -- that is a desperation half-court shot. I thought we could have played 3.6 seconds in the half court.

Keep in mind Butler pretty much MAXIMIZED their attempt with their last shot. The ball was speedily redirected upcourt by Heyward and Howard set a perfect illegal pick to give Heyward that open loo

Great minds think alike!

[MarkD83]

I have not read every post in this thread in detail so I am not sure this has been brought up...Coach K has experienced a lot and often times does things by gut feel and what he remembers.

Last week before the Final Four I rewatched the Duke-UNC game at Duke. Of course Duke was up by 29 and there was only a few seconds left on the clock in the first half so the score did not matter much. However, Nolan Smith hit two free-throws and Duke was in position to play defense. Even so Ginyard had a wide-open look at a 3 from the wing at the buzzer and buried it. Not a significant shot in the UNC game, but my guess is Coach K remembered this play and figured Butler would tie the game on a three if they got a good look, just as he saw Ginyard bury a shot three weeks earlier.

[Reilly]

The simple formula:

Butler's chance of making a scramble 3
vs.
Butler's chance of making a set-up 3 multiplied by Butler's chance of win in OT

I believe Butler had a 5% chance of making a scramble 3, meaning Butler had a 5% chance of winning the game with the strategy K employed.

I believe Butler had a 15% chance of making a set-up 3, and a 50% chance of winning in OT ... so Butler would've had 7.5% chance of victory with the "conventional wisdom" strategy of making the last FT.

K made the right call. He really made the right call if he's correct on Butler's chances in OT and if they were even more than the 50% I assessed them at.

[ACCBBallFan]

This front page article with Mike Francesa goes into great detail onthe analysis

http://www.wfan.com/topic/play_windo...udioId=4543743

Excellent rapport between the other Mike & MIke's